The Crown Prosecution Service is to consider whether any offences were committed when a hoax call was made to the London hospital where the Duchess of Cambridge was receiving treatment.
A nurse fooled by the call, made by two Australian radio presenters, was later found hanged in hospital accommodation.
Jacintha Saldanha had transferred the call to a colleague who then described Kate's condition in detail.
Australia's media watchdog has launched a formal inquiry into the hoax.
Mrs Saldanha answered the call from the 2DayFM presenters in the early hours of the morning on 4 December and, believing them to be members of the Royal Family, put them through to another nurse working at King Edward VII's Hospital.
Mrs Saldanha, a 46-year-old wife and mother-of-two, was found dead three days later. She had left three suicide notes, her inquest revealed as it was opened and adjourned.
The duchess, who is in the early stages of pregnancy, was receiving treatment for hyperemesis gravidarum, an extreme form of morning sickness.
Meanwhile, the Australian Communications and Media Authority is considering if "broadcasting obligations" were breached by the licence-holder for 2DayFM radio station, Today FM Sydney Pty Ltd.
Station owner Southern Cross Austereo has ended the DJs' Hot 30 show and suspended prank calls across the country. It said all profits from advertising for the rest of the year will go into a fund for Mrs Saldanha's family.
The two presenters, Michael Christian and Mel Greig, have said they are "gutted and heartbroken" over the death.
Mrs Saldanha was buried on Monday at a church in her hometown of Shirva, just outside Mangalore on the south-west Indian coast.
Her family accompanied the cortege and were joined by hundreds of mourners.
A spokesman for the Metropolitan Police confirmed that "on Wednesday 19 December, officers submitted a file to the CPS for them to consider whether any potential offences may have been committed by making the hoax call".
However the Met declined to give any details about the nature of any potential offences, adding: "We are not prepared to discuss further."
The CPS has confirmed receiving information from the Met Police and said it would reach a decision in due course.